The error_log files are generated within the 'path' of where the actual error is produced.
If we use WordPress as an example, and your homepage (or any other 'page' of the site), the error_log would be created in the domains public_html.
For example, if this is the main domain of an account, the location would be...
/home/USERNAME/public_html/error_log
However, if the error was something that took place in the wp-admin (which is a directory of its own), then the error_log file would be instead placed in the following...
/home/USERNAME/public_html/wp-admin/error_log
The reason this differs is that the error took place within a subdirectory of the domain.
If you are diagnosing an issue with an addon domain, then the error_log would be placed based on a similar pattern to the above, but from the respective path of the addon domain. For example...
/home/USERNAME/youraddondomain.tld/error_log